Stability Assessment of Power-Converter-Based AC systems by LTP Theory: Eigenvalue Analysis and Harmonic Impedance Estimation

Abstract

Abstract-Stability analysis of power-converter-based AC systems poses serious challenges not only because of the non-linear nature of power converters, but also because linearisation is not generally applied around a steady-state operating point, as in the DC case, but around a time-periodic operating trajectory. Typical examples are single-phase and unbalanced three-phase systems. In this paper, two general methods to assess stability of the aforementioned systems are presented. Both are based on the Linear Time Periodic (LTP) systems theory. The first is model-based and relies on the evaluation of the eigenvalues of the linearised model, assuming a complete knowledge of the parameters. By contrast, the second proposes a set of smallsignal current injections to measure the Harmonic Impedances and applies the LTP Nyquist Criterion, so that stability of the system can be assessed with a black-box approach, without relying on knowledge of the system parameters. The basic LTP systems theory is reviewed in order to provide a mathematical justification for the second method. As case study, a simple network, consisting of a source full-bridge converter in AC voltage-control mode and a load full-bridge converter in AC current-control mode including PLL, is considered. Analytical results based on average modelling and simulations based on both average and switching models are presented, showing good accuracy in the identification of the stability thresholds for both the proposed methods.

Harmonic Stability in Power Electronic-Based Power Systems: Concept, Modeling, and Analysis

“…The wide frequency range of oscillations are tightly coupled with the electric network dynamics, leading to a very high-order system state matrix [67], which consequently imposes a high computational burden for the stability analysis. Moreover, in order to capture the frequency-coupling dynamics of unbalanced threephase power systems, the HSS models of ac-dc converters are required, which also complicates the model derivation process with the increased system order [68].…”

Virtual Inductance for Stable Operation of Grid-Interactive Voltage Source Inverters

“…Hence, two new state equations are added to the controller model in (30) and (31), where according to the control scheme shown in Fig. 5…”

Stability Assessment of High-Bandwidth DC Voltage Controllers in Single-Phase Active Front Ends: LTI Versus LTP Models

“…A comprehensive review of the basics of LTP theory is reported in [31], [32], and only a brief summary is given here, mainly to clarify the notation. Once the steady-state operating conditions have been found from the NLTP system (7), the stability may be determined by linearising the NLTP system around the steady-state periodic operating trajectory [33], [34], which gives an LTP system on which the stability analysis is performed.…”